Exploring Black Holes. - Introduction to General Relativity

General relativity flows from Einstein's field equations, which relate the mass and pressure in a region of spacetime to the "warping" of spacetime across that region. The field equations reveal how this warping is experienced by any observer, whether she is moving, accelerating, rotating, stretching, twisting, or tumbling. The field equations are wonderfully general. But this generality has a price: mathematical sophistication. The field equations speak the language of tensors or differential forms, which closes off this fascinating subject to some people and delays the involvement of others. This book does not start with the field equations but rather with the primary solutions of these equations: the so-called metrics that describe curved spacetime around nonspinning and spinning centers of gravitational attraction. The metric helps to answer every scientific question about (nonquantum) features of spacetime surrounding a black hole, every possible question about trajectories of light and satellites around the black hole as well as around more familiar centers of attraction such as Earth and Sun. The metric for a rotating black hole may tell us about quasars, the most powerful steady energy sources in the Universe. The black-hole metric brings preliminary insights about the history and structure of the Cosmos. Using the metric requires only algebra, elementary differential calculus, and a handful of integrals. This modest mathematics opens the subject to the interested person and paves the way to a deeper study of general relativity for one who will discover new truth about this strange and beautiful Universe, our home. Key idea: Spacetime tells mass how to move; mass tells spacetime how to curve.